Hydrophobicity Regained

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Hydrophobicity regained 1303GAPVIL F MC WYHTSQNEDKR

GAPVIL F MC WYHTSQNEDKRFig. 1. Comparisons of four experimental JG&nl+WaC,cales for the aminoacid side chains. The four scales shown were hased on the soluhilities ofthe free amino acid s in ethanol or dioxane (+ ) (Nozaki & Tanford. 1971).or in N-methyl-acetamide (1)Damodaran & Song. 1986). the partitioningof N-acetyl-amino acid-amides hetween water and octanol ( X ) (Fauchere& Pliska. 1983). and the partitioning of side-chain analogs hetween waterand cyclohexane ( 0 ) Radzicka & Wolfenden, 1988). For each amino acidtype, the variation in is highligh ted by the shaded har. The resi-dues are divided into four groups from left to right based on side-chaincharacteristics: Aliphatic non-hydrogen-honding. aromatic non-hydrogen-honding, sulfur-containing. and hydrogen-bonding.

by any specific interactions that might occur in the target solvent.A weak depend ence on the target environment exists, as theAGknsrervalues for the purely aliphatic side chains (Ala, Pro, Val, Ile, Leu)are roughly 50-75% larger for cyclohexane than for octanol. Th isvariation is due to the combined effects of at least three factors ofunknow n relative importance: octanol contain s ignificant dis-solved water (Radzicka & Wolfenden, 1988). octanol is somewhatpolar, and side chain analogs have different solvation propertiesdue to the absence of the polar main-chain atoms. Which valuesare most relevant for protein folding depends on the relative im-portance of these factors. In any case, the purely aliphatic sidechains have the highest AGEancfer alues in cyclohexane, whereasfor the aromatic (Ph e) and the sulfur containing side chains (Me t,Cys). cyclohexane gives the lowest values. This is consistent witha polarity scale with aliphatic hydrocarbon < aromatic hydrocar-bon < sulfur, and with the assessment that sulfur is a poor hydro-gen bond participant.

In contrast. for the side chains which have one or mo re hydrogenbonding atoms, the AGEan.iferalues diverge, with significantlypositive values in N-methyl-acetamide to large negative values incyclohexane. Th e greatest divergence is seen for the side chainscapable of forming multiple hydrogen bonds. This indicates thatfor these residues the non-aqueous solvent and/or the amino acidanalog have a large effect on the transfer energetics. The likelyexplanation for this scatter is that when polar groups are removedfrom water, they lose favorable hydrogen-bonded interactions withwater. Cyclohexane makes no significant polar interactions (Rad-zicka & Wolfenden, 1988). so the energetics of transfer to cyclo-hexane will reflect the sum of the favorable transfer of the non-polar side chain portions out of water minus the lost hydrogenbonding interactions with water. The AGtansreralues for the othersolvent systems must reflect a similar favorable energy of transferfor the non-polar side chain portions, plus varying amounts ofstabilization of the polar side chain portion through a variety of

interactions. These interactions include intramolecular hydrogenbonding (Roseman, 1988). and hydrogen bonding with the polargroups of the solvent o r residual water that may be dissolved in thesolvent. Independent of the relative contributions of these factors,it is clear that the AG~ancrcralues for polar side chains dependhighly on the environment to which they are transferred!Regaining the original criteria for equatingAG:r(,n.qf,.,nd hydrophobicityThe conceptual foundation for the establishment of a AGEansfer-based hydrophobicity scale for the amino acids was clearly out-lined by Nozaki and Tanford (1971 ):

It has been suggested that 1 0 0 % ethanol can serve as a model'for the inside of a protein molecule . . . ,Le., that the differencein free energy between a hydrophobic moiety in 100% ethanoland in water is simply a measure of the unfavorable free energyof interaction with water, non-specific (van der Waals) inter-actions having about the same free energy in 100%ethanol as inthe interior of a protein molecule. Strong support for this ideacomes from the finding that the free energy of solvent contactsfrom one amino acid side chain (norleucine) differs very littlebetween methanol, ethanol, butanol, and acetone, in contrastto the large difference between any one of these solvents andwater. . . .The forgoing principle cannot of course be applied to molec-ular moieties containing polar groups. Such groups are likely tohave specific interactions with hydroxyl, carbonyl, and otherpolar groups of their environment, and, hence, unlikely to havesimilar free energies in say, ethanol, dioxane, and the inside ofa protein molecule. . . .

For those amino acids which are predominantly hydrophobic(Le., have similar contact free energies in a variety of mediaother than water, and a large positive contact free energy inwater, relative to all such media) the difference between solva-tion free energies in water and in 100% ethanol or other non-aqueous media m ay be con sidered as establishing a hyhphohicityscale.

The parenthetical portion of the last paragraph clearly states twoconditions which must exist for solvent transfer energetics to beequated with hydrophobicity: the AGEan,fer alues must favor thenonaqueous solvent and they must be largely independent of thenonaqueous solvent used. Unfortunately, 25 years of neglect ofthese assumptions was begun by Nozaki and Tanford themselvesas they included the hydrogen bonding side chains Trp, Tyr, His,Thr, and Ser in their "hydrophobicity scale." The inclusion of Trpand Tyr might be understood, because they app eared to fulfill bothcriteria using dioxane and ethanol as reference solvents. but His,Thr, and especially S er certainly did not fulfill the second criterion.Hydrophobicity = AG&,,vf,, on!\,for non-polar groupsBased on the above insights it becomes clear that much debateabout hydrophobicity is due to a neglect of the two conditionsoutlined above. Put simply, equating AGEansferwith hydrophobicity(or solvation free energy) only makes sense for moieties whichtruly are non-polar and it is a misapplication of the paradigm to tryto measure or discussageneric "hydropho bicity" of a polargroup. Such groups simply are not hydrophobic; they do not fi t theparadigm. In this sense, trying to define the "hydrophobicity" of a


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1304hydrogen-bo nding side chain (e.g., arginine) is lik e trying to use asingle color to describe an object which is half blue and half red.Whe reas arguments may be mad e for answers of blue, red, andpurple, the only truly defensible answ er is No, the question is notappropriate; the object is not a single color! Similarly, for thequestion of what is the free energy associated with the removal ofa polar group from water, the only truly justifiable answer is,There is nogenerally valid answ er; it depends on the environmen tinto which it is transferred. This distinction is also supported bythe observation that the en thalpy, entropy, and heat capacity ch angesassociated with the transfer of polar groups to water do not matchthose associated with the hydrophobic effect.Measured AGEansferalues for amphipathic and polar groups arestill highly useful for giving insight into the denaturing or stabi-lizing properties of various solvents relative to water (e.g., Liu &Bolen , 199 5; Tanford, 19 64) because they accurately indicate howmuch better or worse the group in question interacts with thesolvent as opposed to w ater; in this case, the residues environmentinside the folded protein is not relevant. However, suggesting thatthese AGEansferalues have direct relevance for the energetics ofprotein folding or stability is unreasonable because for polar groupsthe AGO values for burial are highly dependent on the final envi-ronment, and each buried group is in a unique environment in theheterogeneous interior of a protein.An important implication of this analysis is that the conceptualfoundation of atom ic solvation parameters (Eisenberg & McLachlan,1986) is flawed because all such parameter sets that include valuesfor polar atoms rest on the invalid assumption that there exists aunique set of AGEansferalues that represent the energetics of theburial of polar groups in a proteins interior. Consistent with thisinsight, two recent reports showed large discrepancies exist be-tween results using atomic solvation parameter sets based on var-ious AGEansferalues (Cummings et al., 1995; Juffer et al., 1995),and others have shown that the use of atomic solvation parametersoften does not contribute to the ability to accurately estimate theenergetics of ligand binding or protein association (Horton & Lewis,1992; Janin, 1995). This insight also gives a reason for the well-documented breakdown of the surface area proportionality for po-lar groups (Lazaridis et al., 1995).A suggested approachThis regaining of the original concept of hydrophobicity makes itclear that using AGEansfer alues to estimate a generic solvationcontribution to the energetics of burial is only valid when dealingwith non-polar groups. As was well documented in the early 1970sand applied extensively since then, the hydrophobicity of hydro-carbon groups is related to accessible surface area with a coeffi-cient of roughly 21-24ca1/A2 for aliphatic groups and 16-19ca1/A2 for aromatic groups (Hermann, 1972; Chothia, 1974; Reyn-olds et al., 1974). For the aliphatic side chains, the range of AGgansfervalues seen between the various solvents shown in Figure 1 cor-responds to a range of -18-32 cal/A2 non-polar accessible sur-face area (Fig. 2). (Corrections suggested by Sharp et al. (1991a,1991b) roughly double these values but the validity of the sug-gested corrections is still being debated (Ben-Naim, 1994; Honig& Yang, 1995 ; Lee, 1995)). Since the middle of this range (25cal/A2) is close to the estimates based on pure hydrocarbons, itseems parsimonious to use that value as an estimate of the hydro-phobic eff ect and accept that there is an uncertainty of roughly+30% (Fig. 2). (This recalls the well-known value of 24 c al/A2

P A . Karplus

,, L~ 00.5 e $0 20 4 0 60 80 100 120accessible surface area

Fig. 2. AG&fe, vs. net side-chain surface area for the four experimentalsystems shown in Fig. 1 (symbols as in Fig. 1). Only the five purelyaliphatic residues are included, with areas taken from Lesser& Rose (1990):Gl y (0A), Ala (39 A), Val (88A), Ile (108 A*), and Leu (1 17 A). Thedashed line represents a comprom ise value for the relationship betweenAGPransfer nd surface area and has a slope of 25 cal/A 2. Based on thearomatic and aliphatic surface area of Phe, it can be calculated that a valueof 16 cal/A is a consensus value between cyclohexane and octanol for theaccessible surface area dependence of aromatic hydrocarbon surface. Bothof these values agree reasonably well with studies of pure hydrocarbons,which have shown aromatic surface to be less hydrophobic than aliphaticsurfaces (Reynolds etal., 1974). Due to the spread of these measurementsthere is some uncertainty associated with the magnitude of the hydrophobiceffect in protein folding but there need be no uncertainty that it is large andfavorable. Two recent reports (Vajda et al., 1995; Chan & Dill, 199 7) makea strong case that a value of near 30-34 cal/A2 (close o that given by thecyclohexane data) is the best value but, until there is a better consensus, thevalue of 25 ? 30% has the advantage of effectively covering the rangeswhich are generally considered as plausible. A range of 33 2 30% doesinclude the low end possibilities but also includes estimates much higherthan are generally considered likely.

value that was suggested by Chothia (1974) but inappropriatelyapplied to both polar and non-polar surface areas based on theexplicit, but often overlooked, assumption that the burial of polaratoms in proteins will contribute 1 kcal/mol more stabilizationenergy than is suggested by the AGEansfer alues measured forethanol.)For the polar parts of amino acid residues, the energetics asso-ciated with burial dep ends heavily on the details of the final en-vironment. Thus, the energetics cannot be estimated by a generichydrophobic effect approach but must be accounted for by acomparison of the final hydrogen-bonding environment with thelost hydrogen bonding with water: Polar groups buried in a poorhydrogen-bonding environment will have very unfavorable ener-getics (like the cyclohexane AGEansfer alues) and those in per-fectly complementary hydrogen bonding environments may makelarge favorable contributions to stability. Whereas the large amountof polar group (especially peptide) burial during protein foldingmeans their energetics are very important (LIU & Bolen, 1995), itseems that estimates of the contribution of polar groups to proteinstability can only be made on an individual basis, with knowledgeof the final environment. Even then, such estimates will be limitedby the accuracy with which polar interaction energies can be cal-culated (Lazaridis et al., 1995). It should be noted that an addi-tional complexity occurring for polar groups is that they do noteven have a generic interaction with water! Multiply hydrogen-bonding substances can have significantly perturbed hydration,


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Hydrophobicity regained 1305which contributes significantly to transfer energetics (Lemieux,1996) and clearly violates additivity principles (Dill, 1997).

In the face of these considerations, a reasonable approach is toignore the polar atom s when accounting for the generic contribu-tions of group burial to stability (this is equivalent to assigningpolar atoms a value of zero in terms of atomic solvation param-eters), and in this way clearly separate the hydrophobic and theenvironment dependent contributions to protein stability. Based onthis simplification, a table can be constructed giving an estim ate ofthe hydrophobic effect expected to be associated with the burial ofeach complete side chain (Table 1) . For non-polar side chains, thereported values are similar to the commonly used values based onAGEansfer.However, for the polar residues, the reported valuesdiffer significantly. A practical application of the values in thistable is forproperly estimating the contribution of the hydrophobiceffect to the change in stability of mutants. For instance, for a

mutation of a buried Lys +A la there is a 2.7kcal/mol discrepancyin accounting for the contribution of the hydrophobic effect: Thenew values show a contribution of 1.0 - 1.9 = -0.9 kcal/molwhich is destabilizing, whereas use of the octanol-based valuesyields a stabilizing contribution of 0.42 - (- 1.35) = 1.77 kcal/mol. This clarification is important for proper accounting of therelative contributions of the hydrophobic effect and hydrogen bond-ing in mutation studies (Pace, 1995).It is worth emphasizing how th e hydrophobicity scale of Table 1relates to the multitude of hydrophobicity scales which are presentin the literature (reviewed in Ponnuswam y, 1993 ). As noted above,the scale presented in Table 1 is a pure hydrophobicity scale in hatit estimates the ree energy due to the hydrophobic effect for trans-fem ng a residue from water to a non-aqueous solvent. All other scalescould be denoted as hydrophobicity plus scales, as each ncludesother factors in addition to the hydrophob ic effect. Direct AGEansfer-

Table 1. Estimated contribution of the hydrop hobic effect to the burial of each type of amino acid residue and sidechain. This table is similar in concept to that presented by Tanford (1962) in which the hyd rophobicity of manypolar side chains was estimated by their non-polar atom content rather than measured AG&,,, values

Residue non-polar Estimated hydrophobic effect Estimated hydrophobic effectsurface areaaor residue burialbor side chain burial AG&fer octanoldResidue type (A2) (kcal/mol)kcal/mol)kcal/mol)GlYAl aValIleLeuProCYSMe tPheTrPTyrHi sTh rSe rGl nAs nGluASPLY sA%

47861351551641244813739 + 155

37 + 19938 + 11643 + 8690566642694512289

1.182.153.383.884.103.101.203.433.464.1 12.812.452.251.401.651.051.731.133.052.23

o.o*1 o2.22.72.91.90.02.32.32.91.61.31.10.20.5

-0.10.5

-0.11.91.1

o.o*0.421.662.452.310.982.091.672.433.061.310.180.35

-0.05-0.30-0.82-0.87- 1.05-1.35- 1.37

T h e hydrocarbon surface areas for the residues were summed from the values given for individual atoms by Lesser and Rose (1990).All surfaces associated with main- and side-chain carbon atoms were included except for amide, carboxylate, and guanidino carbons(main-chain C, C y of Asp, Asn, C6 of Glu, Gln, CJ of Arg). For aromatic side chains, the aliphatic and aromatic surface areas arereported separately. Although the sulfur atoms of Cys and Met may have some truly hydrophobic character, this is not accounted forhere.

bThe magnitude of the hydrophobic effect is assigned to be proportional to apolar surface area alone w ith coefficients of 25 cal/A2for aliphatic carbon atoms and 16 cal/A2 for aromatic carbon atoms (see Fig. 2 legend for the rationale). The true magnitude of thehydrophobic effect is expected to be within ?30% of the value in the table. No account is made for the polar atoms because theircontribution to stability is not governed by the hydrophobic effect. This scale is till an oversimplification because it does not accountfor variations in hydrophobicity fo r carbon atoms bonded to o r near in space to polar atoms. Unfortunately, true values for these atomsmay not be measurable, because the context dependency of the AGkansreralues of polar atoms leads to a n ambiguity in separating theeffects of the polar atom itself from those on the hydrocarbon to which it is adjacent. Although the magnitude is unknown, suchconsiderations would decrease the hydrophobicities of Gly, Ala, Pro, and all the hydrogen-bonding side chains.The values are obtained from the previous column by subtracting the value for Gl y (I . 18 kcal/mol) from each residue. The errorsin these values may, of course, be much larger than 30%. The asterisk denotes that the value for Gly is defined as zero in this and thefollowing scale.dThe values are taken from Fauchere & Pliska (1983), and are probably the most com monly used values f or estimating thecontribution of the hydrophobic effect to changes in stability of mutants. It should be noted that some publications (Creighton, 1994;Ponnuswamy, 1993) of the list mistakenly report the II-values, and these ar e a factor of 1.36 smaller than the freeenergies in kcal/mol.


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1306 PA . Karplusbased scales include the hydrophobic effect plus how well the hy-drogen bonding groups are satisfied by the given non-aqueoussolvent. Scales based on how frequently residue s are buried in pro-teins include the hydrophobic effect plus factors related to proteinstructure and evolution. For instance, it is well known that prolineresidues are buried much less frequently than their chemical hydro-phobicity would predict (Ponnuswamy, 1993).Ashas been noted byLesser and Rose (1990), this is presumab ly because steric andhydrogen-bonding restraints o vem de hydrophobicity considerationsin determining proline placement in proteins. Recognizing the extrafactors present in every hydrophobicity plus scale allows an un-derstanding of why correlations between such scales are far fromperfect. Th e pure hydrophobicity scale is ot better than hydroph o-bicity plus scales, just different. Indeed, whereas the pure hydro-phobicity s cale is useful for estimating th e free energy contributionof the hydrophobic effect, the hydrophobicity plus scales are achuseful for predictions and analyses related to their origin. For in-stance, a burial-based hydrophobicity plus scale is best for pre-dicting w hether or not residues will be buried in a protein.OutlookAs described by Dill (1990b), the true hydrophob ic contribution takesinto accou nt a complete transfer process involving (a) removal ofthe solute from the pure medium, with the breaking of solute-solventbonds, (b) closing the cavity therein, (c) creating a cavity in water,and (d) m aking the solute water bonds.The hydrophobic effect con-tribution to stability does not take into account any environment-dependent effects, such as van der Waals and other non-covalentinteractions in a specific environment in a protein, which may bestronger (or weaker) than the non-bonded interactions present in ageneric non-aqueous solvent. Mutagenesis studies show that suchpacking effects contribute significantly to protein stability (e.g.,Eriksson et al., 1992) but, as with the polar interactions, these arehighly environment dependent and cannot b e assessed in a genericway. It is also possible to place the energetics of polar gro up burialin a similar framewo rk Th e polar groups can be assigned a genericcontribution to stability of 0 kcal/mol, with the actual contributionof each group deviating from zero due to packing effects whichrelate towhether its hydrogen-bonding environment is more or lessfavorable than its interactions with water.

This return to the original concepts related to the quantificationof hydrophobicity by using AGEansferalues should allow the fieldto move beyond questions such as Which solvent system is thebest model for the interior of a protein? The answer is that forpolar groups, no solvent can effectively mimic the heterogeneousinterior of a protein, but for non-polar groups the phenomenon ofhydrophobicity is remarkably robust so that all non-aqueous sol-ventscan be said to be effective mimics, with all amino acidanalogs and solvent systems yielding driving forces within 30%ofthe values obtained in experiments on hydrocarbons. A valid areafor continued research i s to more precisely define where in thisrange the best value for the generic contribution of non-polar aminoacid side chains lies (Vajda et al., 1995; Chan & Dill, 1997).Nevertheless, it should be noted that an accuracy of 30% alreadycompares favorably with current abilities to estimate other majorcontributions to protein stability such as conformational entropyand hydrogen bonding. With this regained formulation, the hydro-phobic effect always contributes favorably and significantly toprotein stability, and it may even be the part of the protein stabilityequation that can be most accurately estimated.

AcknowledgmentsI thank Shing Ho and Victor Shu for fruitful discussions, Ken Dill , HaroldScheraga , and my research group for commentson the manuscript , and theOregon State University Department of Biochemistry and Biophysics forhosting my sabbatical during which these ideas were formulated.his workwas p artially supported by a fellowship from the John Simon GuggenheimMemorial Foundation.ReferencesBen-Naim A. 1994. Solvation: From sm all to macro molecules. Curr Op StructBiol4:264-268.Blokzijl W, Engberts JBFN. 1993. Hydrophobic effects. Opinions and facts.Angew Chem ln r Ed Eng l32: 1545-1579.Chan HS, Dill KA. 1997. Solvation: How to obtain microscopic energies frompartitioning and solvation experiments. Ann Rev Biophys Biomolec Srrucf26. Forthcoming.Chothia C. 1974. Hydrophobic bonding and accessible surface arean proteins.Nature 248338-339.Creighton T. 1994. Proteins: Structures and mole cular proper ties. New York:Freeman Press.Cummings MD, Hart T N, Read RJ. 1995. Atomic solvation parameters in theanalys is of protein-protein docking results. Protein Sci 4:2087-2099.Damodaran S , Song KB. 1986. The r ole of solvent polarity in the free energy oftransfer of amino acid side chains from water to organic solvents. J BiolChem 261:7220-7222.Dill KA. 1990a. Dominant forces in protein folding. Biochemistty 297133-7155.Dill KA. 1990b. The meaning of hydrophobicity. Science 250:297.Dill KA . 1997. Additivity principles in biochemistry. J Biol Chem 272:701-704.Eisenberg D, McLachlan AD. 1986. Solvation energy in protein folding andbinding. Nafure 319199-203.Eriksson AE, Baase WA, Zhang X-J, Heinz DW, Blaber M, Baldwin EP, Mat-thews BW. 1992. Response of a protein structu re to cavity-creating m uta-Fauchere J-L, Pliska V. 1983. Hydrophobic parameters T of amino acid sidetions and its relation to the hydrophobic effect. Science 255178-183.chains from the partitioning of N-acetyl-amino-acid amides. Eu r J Me dHermann RB. 1972. Theory of hydrophobic bonding. 11. The correlation ofChem 18:369-375.hydrocarbon solubility in water with solvent cavity s urfac e area. J PhysChem 7612754-2759.Honig B, Yang A-S. 1995. Free energy balance in protein folding. Adw ProfChem 46:27-55.Horton N , Lewis M. 1992. Calculation of the free energy of association forprotein com plexes. Protein Sci 1 169-1 8 1.Janin J. 1995. Elusive Affinities. Proteins Struct Funct and Genet 2130-39.Juffer AH, Eisenhaber , Hubbard SJ, Walther D, Argos P. 1995. Comparison ofatomic solvation parametric sets: Applicability and imitations in proteinfolding and binding. Protein Sci 4:2499-2509.Kauzmann W. 1959. Some factors in the interpretation of protein denaturation.Adv Prot Chem 14:l-63.Lazaridis T, Archontis G, Karplus M. 1995. Enthalpic contribution to proteinstability: Insights from atom-based c alculatio ns and statistical mechanics.Adv Prot Chem 47231-296.Lee B. 1995. Analy zing solvent reorganization and hydrophobicity. Meth En-zymol 259555-576.Lemieux RU. 1996. How w ater provides the impetus for mo lecular recognitionLesse r GJ, Rose GD . 1990. Hydrophobicity of amino acid subgroup s in pro-in aqueous solution. Acc Chem Res 29373-380.

Liu Y, Bolen DW. 1995. The peptide backbone plays a dominant role in proteinteins. Proteins Struct Funcr Genet 86-13.stabilizatio n by naturally occurring osmolytes. Biochemistry 34: 12884-12891.Makhatadze GI, Privalov PI. 1995. Energetics of protein structure. Adv ProfChem 47307-417.Nozaki Y, Tanford C. 1971. The solubility of amino acids and two glycine2217.peptides in aqueous ethanol and dioxane olutions. J Biol Chem 246:2211-Pace CN. 1995. Evalu ating the contribution of hydrogen bonding and hydro-

Ponnuswam y PK. 1993. Hydrophobic characteristics of folded proteins. Progphobic bonding to protein folding. Meth Enzymol 259:538-554.

Radzicka A, Wolfenden R. 1988. Comparing the polarities of the amino acids:Biophys Molec Biol 5957-103.side-chain distribution coefficients between the vapor phase, cyclohexane.I-octanol, and neutral aqueous solution. Biochemistry 2 7 1664-1670.Reynolds JA, Gilbert DB, Tanford C. 1974. Empirical correlation between hy-


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Rose GD, Wolfenden R. 1993. Hydrogenbonding, hydrophobicity, packing, andprotein folding. An n Rev Biophys Biomol Strucf 22:381-415.Roseman MA. 1988. Hydrophobicity of polar amino acid side chains is mark-edly reduced by flanking peptide bonds. J Mo l Biol 200513-522.Sharp K A , Nicholls A, Fine RF, Honig B. 1991a. Reconciling the magnitude ofthe microscopic and macroscopic hydrophobic effects. Science 252: 106-109.Sharp KA , Nicholls A, Freidman R, Honig B. 1991b. Extracting hydrophobic

USA 71:2925-2927. free energie s from experim ental data: Relationship to protein folding andtheoretical models. Biochemisfry 30:9686-9697.Tanford C. 1962. Contribution of hydrophobic interactions to he stability of th eglobular conformation of proteins. J Am Chem Soc 844240-4247.Tanford C. 1964. Isothermal unfolding of globu lar proteins n aqueou s ureasolutions. J Am Chem Soc 862050-2059.Vajda S, Weng Z, DeLisi C. 1995. Extracting hydrophobicity parameters fromsolute partition and protein mutation/unfolding experiments. Protein Engi-neering 8:1081-1092.

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